Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi$-variation in the sense of Wiener

J. A. Guerrero, J. Matkowski, and N. Merentes. "Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener." Commentationes Mathematicae 50.1 (2010): null. <http://eudml.org/doc/291532>.

@article{J2010,
abstract = {Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener $\varphi $-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.},
author = {J. A. Guerrero, J. Matkowski, N. Merentes},
journal = {Commentationes Mathematicae},
keywords = {$$-variation in the Wiener sense; composition operator; uniformly continuous operator; left-left regularization; Jensen equation},
language = {eng},
number = {1},
pages = {null},
title = {Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener},
url = {http://eudml.org/doc/291532},
volume = {50},
year = {2010},
}

TY - JOUR
AU - J. A. Guerrero
AU - J. Matkowski
AU - N. Merentes
TI - Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi $-variation in the sense of Wiener
JO - Commentationes Mathematicae
PY - 2010
VL - 50
IS - 1
SP - null
AB - Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener $\varphi $-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.
LA - eng
KW - $$-variation in the Wiener sense; composition operator; uniformly continuous operator; left-left regularization; Jensen equation
UR - http://eudml.org/doc/291532
ER -